Chapter 5.8, Problem 33PPE

To determine

To Graph: The given function by translating $y=\left|x\right|$ and to describe the relation between them.

Explanation of Solution

Given information:

The given function is $y=|x-1|+2$

Consider $y=\left|x\right|=\{\begin{array}{l}-x;x<0\\ x;x\ge 0\end{array}$

Graph:

The graph of $y=|x-1|+2$ is shown below.

  

The graph of $y=|x-1|+2$ is the $1$ unit right shift followed by $2$ units up shift of the graph of $y=\left|x\right|$

Hence, the graph of the given function is drawn by translating $y=\left|x\right|$ .